Groupoid algebras as covariance algebras

2019/06/07 by Clark, Lisa Orloff, Fletcher, James
#46L05 #46L08 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1906.02855

Abstract

Suppose G is a second-countable locally compact Hausdorff étale groupoid, G is a discrete group containing a unital subsemigroup P, and c:G→ G is a continuous cocycle. We derive conditions on the cocycle such that the reduced groupoid C^*-algebra C_r^*(G) may be realised naturally as the covariance algebra of a product system over P with coefficient algebra C_r^*(c^-1(e)). When (G,P) is a quasi-lattice ordered group, we also derive conditions that allow C_r^*(G) to be realised as the Cuntz--Nica--Pimsner algebra of a compactly aligned product system.

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